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Physics 111physics.valpo.edu › courses › p111 › lectures › lecture10notes.pdfProof in the...
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1 Physics 111 Tuesday, September 28, 2004 • Ch 6: Circular Motion - centripetal acceleration Friction Tension - the massless string Help this week: Wednesday, 8 - 9 pm in NSC 128/119 Sunday, 6:30 - 8 pm in CCLIR 468 Announcements Tues Sept .28. Phys 111 Don’t forget to read over the lab write-up and be ready for the quiz. Announcements Tues Sept .28. Phys 111 Note the following: How does your weight change while you’re… • Ascending? • Descending? • Decelerating? • Accelerating? Ch 4: Newton’s Laws Tues Sept .28. Phys 111 Applications of Newton’s Laws I will NOT cover everything in this chapter… Now that we have seen and applied Newton’s Laws (at least a few times), let’s introduce a couple of new forces. Ch 6: Applying Newton’s Laws Tues Sept .28. Phys 111 Uniform Circular Motion: the “speed” of the object does not change, but the object is accelerating throughout the motion. | v| = constant v ≠ constant But... Ch 6: Applying Newton’s Laws Tues Sept .28. Phys 111
Transcript of Physics 111physics.valpo.edu › courses › p111 › lectures › lecture10notes.pdfProof in the...
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Physics 111
Title page
Tuesday,September 28, 2004
Physics 111 Lecture 10
• Ch 6: Circular Motion - centripetal accelerationFrictionTension - the massless string Help this week:
Wednesday, 8 - 9 pm in NSC 128/119Sunday, 6:30 - 8 pm in CCLIR 468
Help sessions
AnnouncementsTuesSept
.28.Phys111
Don’t forget to read over the labwrite-up and be ready for the quiz.
labs
AnnouncementsTuesSept
.28.Phys111
Note the following:
How does your weightchange while you’re…
• Ascending?• Descending?• Decelerating?• Accelerating?
Elevator experiment results?
Ch 4: Newton’s LawsTuesSept
.28.Phys111
Applications of Newton’s Laws
I will NOT cover everything in this chapter…
Ch 6
Now that we have seen and applied Newton’sLaws (at least a few times), let’s introduce acouple of new forces.
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Uniform Circular Motion: the “speed” of theobject does not change, but the object isaccelerating throughout the motion.
|v |= constant
v ≠ constant
But...
Uniform circular motion
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
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2
Tangential acceleration
For an object moving in acircle, the instantaneousvelocity vectors are alwaystangent to the circle ofmotion!
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Uniform Circular Motion: the “speed” of theobject does not change, but the object isaccelerating throughout the motion.
Although our objects movesin a circle at constant speed,it still accelerates.
WH
Y?
Recall that acceleration and velocity areboth vector quantities. Since accelerationis a change in velocity over a change intime, an object with a velocity thatchanges direction is accelerating!
Centripetal acceleration
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Proof in the book and in class notes.
|a ||v|
c
=2
r
where r is the radius of the circleand |v| the speed of the object.
a vc⊥
Centripetal acceleration def.
rv
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Recall our definitionof acceleration:
a =
Δt→0lim
ΔvΔt
=t f →tilim
v
f− v
i
tf− t
i
ri rf
r
f ri
Δr
Δθ
v
i
v
f
Color Code: velocity; position in yellow; acceleration
Diagram of cent. Acc.
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Velocity Vectors
Again, we’re using vector subtraction(remember, subtracting one vector fromanother is like adding its negative).
v
i
v
f
Δv
Δθ
By geometry, this angleis the same as that onthe last slide betweenthe position vectors!
Now, we’ve got two similar, isosceles triangles.
Velocity vectors
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
| Δr ||r |
= | Δv |
|v |
Now, returning to our definition of acceleration
|a
c|=
Δt→0lim
| Δv |Δt
=
Δt→0lim
|v || Δr |(Δt) r
= |v |2
r
r
f ri
Δr
Δθ
v
i
v
f
Δv
Δθ
A sub c
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Notice that as Δt → 0, the vector pointstowards the exact center of the circle.
Δv
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3
For an object moving in acircle with a constant speed,we can define a periodassociated with the motion.
The period of therotation is simplythe time requiredfor the object to goaround the circleexactly one time.
Td r= =|v| |v|
2π
period
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
T = 2πr
|v |
[T ] = [2πr]
[|v |]
[T ] = m
m/s= sThat’s good. We knew
period had to haveunits of time.
[period]
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
A ball of mass m on theend of a string is movingin a circle. We know thatthe ball is experiencingan acceleration.
Newton’s 2nd Law tells us that in order for anobject to experience an acceleration, a netexternal force must be acting.
m
top view
Centripetal force
T
ac
v
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Worksheet Problem #1
CQ1 stick to the wall
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
NOTE!
Newton’s 2nd Law takes on a slightly differentform for problems involving circular motion.
In these problems, Newton’s 2nd Law says
F mamv
rnet c= =
2
(inward)
Newton’s 2nd Law
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
An automobile with mass 1500-kg moves at aconstant speed over the crest of a hill. Thedriver moves in a vertical circle of radius 28.0 m.At the top of the hill, she notices that the carbarely maintains contact with the road. Find thespeed of the vehicle.
?P1 automobile Motion Diagram
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Problem Solving Worksheet
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4
W2: 1st Law via demos
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
• Block across the floor at constant speed. Why is it not accelerating?
Let’s look at a couple of demosinvolving blocks sliding acrossthe floor. Again, use FBD’s tohelp you understand the motion.
• Block across the floor after push. Why does it stop?
Class Worksheet #2: Block Predictions
What is friction?
A macroscopic (meaning, observable to the eye)force that operates at the interface between twosurfaces in a direction to oppose the slipping ofthose surfaces across one another.
As I push on the red blockwith some force, frictionwith the surface of the blueblock acts to prevent thered block from sliding.
Friction 1
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
What is friction?
First, make a pictorial representation anddescribe the forces present.
Friction 1
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
N = normal forceof bottom block ontop block
W = Weight or thegravitational forceof Earth on block
fs = frictionalforce of bottomblock on top block
Fext = the externalforce pushing theblock
What is friction?
Now let’s draw the FBD for the red block…
Friction 1
W
n
f
s
F
ext
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
The frictional force at theboundary is described asthe force of static friction,as it relates to the forceobserved on a pair ofobjects that do not sliprelative to one another.
We find that experimentally, the magnitude ofthe maximum force of static friction isproportional to the normal force exerted by theblue block on the red block.
static friction
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Fext
fs
The constant of proportionality is known asthe coefficient of static friction (µs) and is aproperty of the materials at the interface.
static friction
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Fext
fs
The frictional force at theboundary is described asthe force of static friction,as it relates to the forceobserved on a pair ofobjects that do not sliprelative to one another.
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5
If I push hard enough,the force of static frictionwill be broken and slippingwill occur at the interface.The red block will begin toaccelerate relative to theblue block.
When the red block slips, we note that it stillfeels a frictional force. The magnitude ofthat force, however, has changed.
kinetic friction
a
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Fext
fk
We find experimentally that the themaximum value of new frictional force isstill proportional to the normal force exertedby the blue block on the red block.
kinetic friction
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
If I push hard enough,the force of static frictionwill be broken and slippingwill occur at the interface.The red block will begin toaccelerate relative to theblue block.
a Fext
fk
This force is describedas the force of kineticfriction, as it relates tothe force observed ontwo objects that sliprelative to one another.
The constant of proportionality is known asthe coefficient of kinetic friction (µk) and is aproperty of the materials at the interface.
kinetic friction
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
a Fext
fk
CQ3 Friction: sliding box
Worksheet Problem #3
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
both frictional forces
The frictional forces are always directed so as tooppose the slippage between the two surfaces.
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Fext
fs ≤ µs
n
Static Case:Object at rest
f
s
Fext
f nk k= µ
Kinetic Case:Object in Motion
v
f
k
CQ4 Friction: tilting plane
Worksheet Problem #4
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
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Does friction always result in anobject slowing down?
Let’s look at a couple of examples to find out...
What’s going to happen to the green objectas I push the blue book across the table?
Consult with neighbors.
friction causes motion? (W#5a)
Worksheet Problem #5a
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
Consult with neighbors.Worksheet Problem #5b
Does friction always result in anobject slowing down?
Let’s look at a couple of examples to find out...
What happened to the green object this timeas I pushed the blue book across the table?
second example (W#5b)
Ch 6: Applying Newton’s LawsTuesSept
.28.Phys111
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